The narrow gravel road to Johnson Lake is open only for the summer months. At pr
ID: 2675448 • Letter: T
Question
The narrow gravel road to Johnson Lake is open only for the summer months. At present the county spends $750 per mile each year to prepare the road for summer traffic and another $150 per mile for maintenance during the period in which it is open. A "permanent" road could be constructed at a cost of $10,000 per mile'; the county would have to spend $800 per mile for maintenance only every 5 years through the 30 year life of the road. prospects for the area suggest that the road would have to be relocated at the end of that period. If 8% is reasonable discount rate, which option is less costly? what discount rate would cause the two alternatives to have the same cost in the present value terms. Please show workExplanation / Answer
Option 1 For a thirty year period Present value of all the costs = 900/1.08 + 900/1.08^2.....+900/1.08^30 =$10,132.01 Option 2 Present value of all the costs = 10,000/1.08 + 800/1.08^5 +800/1.08^10.....+800/1.08^30 =$12,683.61 Option 1 is less costly To find the discount rate at which two options are equally attractive 900/(1+r)+ 900/(1+r)^2.....+900/(1+r)^30 = 10,000/(1+r) + 800/(1+r)^5 +800/(1+r)^10.....+800/(1+r)^30 r= 5.3475%